The value of a cone is 27 cm to the third power. What is the value of the cylinder that shares the same radius in height as the cone
To find the value of the cylinder that shares the same radius and height as the cone, we first need to determine the volume of the cone and then use that value to calculate the volume of the cylinder.
The formula for the volume of a cone is given by: V_cone = (1/3) * π * r^2 * h, where r is the radius and h is the height of the cone.
Given that the volume of the cone is 27 cm³, we have: 27 = (1/3) * π * r^2 * h.
Since the cylinder has the same radius and height as the cone, we can denote them as r_cy and h_cy, respectively.
Therefore, the volume of the cylinder can be expressed as: V_cylinder = π * r_cy^2 * h_cy.
Since we know that r_cy = r and h_cy = h, we can substitute these values into the equation.
V_cylinder = π * r^2 * h.
Now, we need to calculate the value of V_cylinder using the volume of the given cone.
Given that V_cone = 27 cm³, we can rewrite the equation as:
27 = (1/3) * π * r^2 * h.
To solve for r^2 * h, we can isolate this term by multiplying both sides of the equation by 3/π:
r^2 * h = (3/π) * 27.
Simplifying, we get:
r^2 * h = 3 * 27 = 81.
Now, we substitute this value into the equation for the volume of the cylinder:
V_cylinder = π * 81.
Thus, the value of the cylinder that shares the same radius and height as the given cone is π * 81 cm³.